8. Tuna Fish The tuna fish data from Exercise 14

(Section 11.2) were analyzed as a completely randomized design with four treatments. However we could also view the experimental design as a 232 factorial experiment with unequal replications. The data are shown below

The data can be analyzed using the model

where 0 1 x 5 if oil, 1 if water 0 2 x 5 if light tuna, 1 if white tuna

a. Show how you would enter the data into a computer spreadsheet, entering the data into columns for y, 1 x , 2 x , and 1 2 x x .

b. The printout generated by MINITAB is shown below.
What is the least-squares prediction equation?

c. Is there an interaction between type of tuna and type of packing liquid?

d. Which, if any, of the main effects (type of tuna and type of packing liquid) contribute significant information for the prediction of y?

e. How well does the model fit the data? Explain.

oll Water Light Tuna 2.56 1.92 1.30 1.79 1.23 292586 .99 1.12 .66 1.92 .63 1.23 .67 .65 .85 .69 .60 .65 .60 .67 .53 .60 1.41 .66 White Tuna 1.27 1.22 1.19 1.22 1.49 1.29 1.29 1.00 1.27 1.27 1.35 1.28 Source: Case Study"Tuna Goes Upscale" Copyright 2001 by Consumers Union of U.S., Inc., Yonkers, NY 10703-1057, a nonprofit organization. Reprinted with permission from the June 2001 issue of Consumer Reports for educational purposes only. No commercial use or reproduction permitted. www.Consum- erReports.org.